Abstract
Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving the hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic functions - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h → −∞.
Highlights
Soil sorptivity represents the capacity of a soil to absorb or desorb liquid by capillarity, and is one of the key factors for modeling water infiltration into soil or flow in the vadose zone (Cook and Minasny, 2011)
We considered three commonly used hydraulic models, for which Lassabatere et al (2021) proposed analytical formulations for S (−∞, 0): Brooks and Corey (BC), van Genuchten - Burdine, and van Genuchten - Mualem
240 In this study, we aim to demonstrate the following points: (i) the studied hydraulic models for water retention (WR) and hydraulic conductivity (HC) functions exhibit challenging conditions for the computation of sorptivity, (ii) the proposed mixed formulation is an ideal estimator for sorptivity, and (iii) the usual methods, based on the use of SK and SD (Eq 2 and Eq 1), or their improved version, SK−V2 and SD−V2 (Eq 13 and Eq 19) do not necessarily provide accurate estimations of the targeted nominal sorptivity
Summary
Soil sorptivity represents the capacity of a soil to absorb or desorb liquid by capillarity, and is one of the key factors for modeling water infiltration into soil or flow in the vadose zone (Cook and Minasny, 2011). (Angulo-Jaramillo et al, 2016; Stewart and Abou Najm, 2018). Several models and methods make use of this variable such 15 as in the the Beerkan Estimation of Soil Transfer parameters (BEST) methods (Lassabatere et al, 2006, 2009, 2014, 2019; Angulo-Jaramillo et al, 2019) and related simplified Beerkan approaches (Bagarello et al, 2014b; Di Prima et al, 2020; Yilmaz, 2021). Sorptivity is required for the computation of several hydraulic parameters, like the macroscopic capillary length (Bouwer, 1964; White and Sully, 1987). Parlange (1975) proposed an accurate approximation for the quantification of sorptivity: θ1
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